After days of criticism that he was excluding Republicans from immigration talks, President Barack Obama on Tuesday reached out to several Republican leaders who are calling for an overhaul of the nation’s immigration system.

After days of criticism that he was excluding Republicans from immigration talks, President Barack Obama on Tuesday reached out to several Republican leaders who are calling for an overhaul of the nation’s immigration system.

According to the White House, Obama called Sens. Marco Rubio of Florida, Lindsey Graham of South Carolina and John McCain of Arizona to “discuss their shared commitment to immigration reform.”

“The president reiterated that he remains supportive of the effort underway in Congress and that he hopes that they can produce a bill as soon as possible that reflects shared core principles on reform,” the White House said.

A war of words blew up between Republicans and the White House on Tuesday, two days after the leaking of an administration legislative blueprint on immigration that was discussed on the Sunday news talk shows.

Rubio, through his staff, told reporters that his office had had no discussion with the White House on immigration.

“Contrary to what the WH COS (White House Chief of Staff Denis McDonough) said on the Sunday shows, President Obama and the White House staff are not working with Republicans on immigration reform. Senator Rubio’s office has never discussed immigration policy with anyone in the White House,” Rubio spokesman Alex Conant said in an email to reporters early Tuesday.

The White House disputed the contention. White House spokesman Jay Carney said later that the administration has been “working with every member’s office that’s involved in the Gang of Eight process.”

Conant responded that the administration has sent agency officials to brief staff at the bipartisan group meetings, but “they’ve never asked for our input.”

Obama has often said his “door is always open” on immigration and other issues, but rarely does he meet with Republicans. Obama has held meetings with Democratic leaders, union heads and advocacy groups on immigration.

Obama met Feb. 13 with the four Democrats in the Senate – Charles Schumer of New York, Robert Menendez of New Jersey, Michael Bennet of Colorado and Richard Durbin of Illinois – who are helping to lead their chamber’s immigration overhaul. The four Republicans senators – Rubio, McCain, Graham and Jeff Flake of Arizona – were not invited to attend, according to Don Stewart, a spokesman for Senate Minority Leader Mitch McConnell.

On Tuesday’s call, the White House said, Obama commended the senators for the bipartisan progress that continues to be made by the Gang of Eight, as the bipartisan group of senators is known.

“The president reiterated that he remains supportive of the effort underway in Congress, and that he hopes that they can produce a bill as soon as possible that reflects shared core principles on reform. The president has made clear that he believes commonsense reform needs to include strengthening border security, creating an earned path to citizenship, holding employers accountable and streamlining legal immigration,” the White House said.

Rubio received Obama’s call late Tuesday night in Jerusalem. Conant said Rubio appreciated the call.

“The senator told the president that he feels good about the ongoing negotiations in the Senate and is hopeful the final product is something that can pass the Senate with strong bipartisan support,” Conant said.

Kevin Bishop, a spokesman for Graham, said the South Carolina Republican heard from the president in the afternoon.

“Sen. Graham had a short, cordial phone conversation with President Obama,” Bishop said. “They discussed the need for immigration reform and why it is important we fix our broken immigration system.”